Specifically, according to the original article:
Sources say that officials in Beijing warned Air New Zealand to remove reference to any paperwork which suggested Taiwan was a state back in 2018, but someone forgot to do so.
The problem related to documentation from New Zealand's Civil Aviation Authority which was included as part of Air New Zealand's application to allow the particular plane to land in China. According to sources "the Chinese were very explicit" about what the issue was, however the issue was not resolved. The source added that the airline "could have cast a political lens" over the CAA documentation but did not do so.
CAA disputed the version of events, without giving details.